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What about usage of Mobility Patterns? Visual analytics for mobility data

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 9 Visual analytics for mobility data [Andrienko et al. 2007] What is an appropriate way to visualize groups of trajectories?

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 10 Summarizing a bunch of trajectories 1) Trajectories  sequences of “moves” between “places” 2) For each pair of “places”, compute the number of “moves” 3) Represent “moves” by arrows (with proportional widths) Major flow Minor variations Many small moves

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A word on uncertainty

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 12 Handling Uncertainty Handling uncertainty is a relatively new topic! A lot of research effort has been assigned  Developing models for representing uncertainty in trajectories. The most popular one [Trajcevski et al. 2004]: a trajectory of an object is modeled as a 3D cylindrical volume around the tracked trajectory (polyline) Various degrees of uncertainty

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Coming back to our approach

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 14 Challenge 1: Introduce trajectory fuzziness in spatial clustering techniques  The application of spatial clustering algorithms (k-means, BIRCH, DBSCAN, STING, …) to Trajectory Databases (TD) is not straightforward  Fuzzy clustering algorithms (Fuzzy C-Means and its variants) quantify the degree of membership of each data vector to a cluster  The inherent uncertainty in TD should taken into account. Challenge 2: study the nature of the centroid / mean / representative trajectory in a cluster of trajectories.  Is it a ‘trajectory’ itself? Motivation

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 16 From Fuzzy sets to Intuitionistic fuzzy sets Definition 1 (Zadeh, 1965). Let a set E be fixed. A fuzzy set on E is an object of the form Definition 2 (Atanassov, 1986; Atanassov, 1994). An intuitionistic fuzzy set (IFS) A is an object of the form where and where

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 17 Hesitancy For every element The hesitancy of the element x to the set A is

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 36 Conclusions We proposed a three-step approach for clustering trajectories of moving objects, motivated by the observation that clustering and representation issues in TD are inherently subject to uncertainty.  1 st step: an intuitionistic fuzzy vector representation of trajectories plus a distance metric consisting of a metric for sequences of regions and a metric for intuitionistic fuzzy sets  2 nd step: Algorithm CenTra, a novel technique for discovering the centroid of a bundle of trajectories  3 rd step: Algorithm CenTR-I-FCM, for clustering trajectories under uncertainty

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 37 Future Work Devise a clever sampling technique for multi-dimensional data so as to diminish the effect of initialization in the algorithm; Exploit the metric properties of the proposed distance function by using an distance-based index structure (for efficiency purposes); Perform extensive experimental evaluation using large trajectory datasets

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 42 Temporal focusing Different time intervals can show different behaviours  E.g.: objects that are close to each other within a time interval can be much distant in other periods of time The time interval becomes a parameter  E.g.: rush hours vs. low traffic times Already supported by the distance measure  1,  2  Just compute D(  1,  2 ) | T on a time interval T’  T Problem: significant T’ are not always known a priori  An automated mechanism is needed to find them

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 43 The representative trajectory of the cluster:  Compute the average direction vector and rotate the axes temporarily.  Sort the starting and ending points by the coordinate of the rotated axis.  While scanning the starting and ending points in the sorted order, count the number of line segments and compute the average coordinate of those line segments. TRACLUS – representative trajectory

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Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World" 44 Trajectory Uncertainty vs. Anonymization Never Walk Alone [Bonchi et al. 2008]  Trade uncertainty for anonymity: trajectories that are close up the uncertainty threshold are indistinguishable  Combine k-anonymity and perturbation Two steps:  Cluster trajectories into groups of k similar ones (removing outliers)  Perturb trajectories in a cluster so that each one is close to each other up to the uncertainty threshold